\documentclass{minimal}
\usepackage{amsmath}
\usepackage{hyperref}

\begin{document}

$a_1$
$a_+$
$a_-$
$a_=$
$a_{i + 1}$
$a_{i+1}$
$a_{\beta k}$
$a_{\hat k}$

$a^1$
$a^+$
$a^-$
$a^=$
$a^{i + 1}$
$a^{i+1}$
$a^{\hat k}$

\begin{equation}
  \bigl\lvert x \bigr\rvert
  \operatorname{test}(a) = 1
\end{equation}

$\langle \| \\ \rangle$

% Concealed and styled (bold; italic)
\textup{asd $\alpha$}
\textbf{test}
\textit{test}
\textsl{test}
$4 \mathit{x} = \mathbf{test}$
$\mathrm{Re} = \cdots$

\begin{equation}
  \mathbb{P}(x \,|\, y) \!= \dots
\end{equation}

$\bar a$
$\bar{a}$

\begin{equation}
  \text{test}
  \textnormal{test $asd$}
  \textrm{test}
  \textup{test}
  \texttt{test}
  \textsf{test}
  \textsc{test}
\end{equation}

\href{url}{text}

\keyw{Piecewise \textbf{test} splines}

\end{document}
